1. Field of the Invention
The present invention relates to a method for the quality control of printed products. In particular the invention relates to a method for checking the color reproduction accuracy of a given printer in view of color fading.
2. Description of the Related Art
The invention relates to the field of image rendering by means of multidimensional color reproduction devices. The independent values with which the color device can be addressed are called colorants or inks. For purposes of generality, the physically achievable values for these colorants range from 0 to 100%. A color reproduction device with n colorants will be called a printer or an n-ink process.
A typical device we have in mind is a multidimensional color printer with n colorants such as a CMYK offset printing press, but the invention can also be applied to other color reproduction devices, including multi-primary color displays.
With colorant space is meant an n-dimensional space with n the number of independent variables with which the printer can be addressed. For the offset printing press the dimension of the space corresponds to the number of inks of the printer, which is usually four.
With color space is meant a space that represents a number of quantities of an object that characterize its color. In most practical situations, colors will be represented in a 3-dimensional space such as the CIE XYZ space. However, also other characteristics can be used such as multispectral values based on filters that are not necessarily a linear transformation of the color matching functions to represent color. A typical example is an m-dimensional space of which the axes correspond to densities.
To characterize the color of object colors, it is nowadays common to measure the reflectance curve instead of directly the color values. For emission colors, the spectral power distribution is recorded. To convert the spectral data to color values the viewing conditions have to be specified. The minimum set of viewing conditions commonly used are the Color Matching Functions (CMF) and the viewing illuminant. In Graphic Arts, the standard values for these viewing conditions are the CIE 2 degree standard observer and the standard D50 illuminant. The obtained color values are referred to as tristimulus values and they are considered as a unique specification of a color for the Human Visual System (HVS) of a standard observer. The conversion from spectral data to tristimulus values is obtained as follows:
      X    =          100      ⁢                                    ∫            360            830                    ⁢                                    R              ⁡                              (                λ                )                                      ⁢                          I              ⁡                              (                λ                )                                      ⁢                          X              ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                                            ∫            360            830                    ⁢                                    I              ⁡                              (                λ                )                                      ⁢                          Y              ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                                Y    =          100      ⁢                                    ∫            360            830                    ⁢                                    R              ⁡                              (                λ                )                                      ⁢                          I              ⁡                              (                λ                )                                      ⁢                          Y              ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                                            ∫            360            830                    ⁢                                    I              ⁡                              (                λ                )                                      ⁢                          Y              ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                                Z    =          100      ⁢                                    ∫            360            830                    ⁢                                    R              ⁡                              (                λ                )                                      ⁢                          I              ⁡                              (                λ                )                                      ⁢                          Z              ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                                            ∫            360            830                    ⁢                                    I              ⁡                              (                λ                )                                      ⁢                          Y              ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                          
In which:                lambda is the wavelength, ranging theoretically from        360 to 830 nanometers and wherein:        R(lambda) is the reflectance curve        I(lambda) is the power spectrum of the illuminant        X(lambda), Y(lambda) and Z(lambda) are the color matching functions of the standard observer.        
With colorant gamut or colorant domain is meant the delimited space in colorant space of colorant combinations that are physically realizable by a given printer, taking into account possible extra limitations on colorant combinations.
The colorant gamut of a CMYK offset press for example is delimited by a linear condition that limits the sum of the four colorants (for example to 340%).
A printer model is a mathematical relation that expresses color values in function of colorants for a given printer. The variables for the colorants are denoted as c1, c2, . . . , cn with n the dimension of the colorant space.
An n-ink process is completely characterized by its colorant gamut with a number of colorant limitations and the printer model. Because of this close relationship between an n-ink process and the printer model, the operations typical for a printer model are also defined for the n-ink process. With inverting an n-ink process is meant that the corresponding printer model is inverted. The transformation of an n-ink process to color space on the other hand is equivalent to transforming the corresponding colorant domain to color space by making use of the printer model.
With color gamut is meant a delimited region in color space, containing colors that are physically realizable by a given printer, taking into account possible extra limitations on colorant combinations.
Metameric color patches are colors that have a different spectral characterization but the same color values. Typically we think about surface colors with different reflectance spectra but the same XYZ values for a given set of viewing conditions. In a similar way, for multi-primary color displays, i.e. color displays with more than three primaries, metameric colors can be generated.
Color Checks
To check the color reproduction behavior of a printer, typically a number of color patches are printed and measured, and compared with reference values. If the color difference is too large, it is recommended to recalibrate the system. If this does not help, the printer should also be characterized again.
The main problem with checking the state of the printer by printing and measuring a number of color patches is that mismatches are not found easily. A spectro-photometer or colorimeter is needed and an application has to be used to calculate the color differences.
However, if a color mismatch is caused by a difference between the real viewing conditions and the viewing conditions for which a color match was calculated, such a mismatch will not be detected by printing and measuring a number of color patches using standard procedures, because these always assume standard viewing conditions.
And finally, if only the viewing conditions have to be checked, dedicated strips can be bought indicating if an illuminant is still behaving as a predefined standard. However, as these strips are typically made to check if an illuminant id D50 like, they cannot be used to check the stability of custom illuminants.